Affine Gaudin models and hypergeometric functions on affine opers

DOI10.1016/j.aim.2019.04.032zbMath1459.17043arXiv1804.01480OpenAlexW2964160615WikidataQ127918590 ScholiaQ127918590MaRDI QIDQ2421255

Sylvain Lacroix, Benoît Vicedo, Charles A. S. Young

Publication date: 14 June 2019

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.01480

zbMATH Keywords

hypergeometric integralsBethe ansatzGaudin modelaffine opers

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Exactly solvable models; Bethe ansatz (82B23) Hypergeometric functions associated with root systems (33C67)

Related Items (13)

Quartic Hamiltonians, and higher Hamiltonians at next-to-leading order, for the affine sl2 Gaudin model ⋮ 4D Chern-Simons theory and affine Gaudin models ⋮ Four-dimensional Chern–Simons theory and integrable field theories ⋮ Geometric aspects of the ODE/IM correspondence ⋮ Constrained affine Gaudin models and diagonal Yang–Baxter deformations ⋮ On a class of conformal \(\mathcal{E}\)-models and their chiral Poisson algebras ⋮ Higher current algebras, homotopy Manin triples, and a rectilinear adelic complex ⋮ Integrable sigma models at RG fixed points: quantisation as affine Gaudin models ⋮ An analog of the Feigin-Frenkel homomorphism for double loop algebras ⋮ ODE/IQFT correspondence for the generalized affine \(\mathfrak{sl} (2)\) Gaudin model ⋮ Opers for higher states of quantum KdV models ⋮ Kondo line defects and affine Gaudin models ⋮ Affine opers and conformal affine Toda

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Integrable structure of quantum field theory: classical flat connections versus quantum stationary states
• Cyclotomic Gaudin models: construction and Bethe ansatz
• Bethe ansatz and the spectral theory of affine Lie algebra-valued connections. II: The non simply-laced case
• Quantum integrable model of an arrangement of hyperplanes
• Opers with irregular singularity and spectra of the shift of argument subalgebra
• ODE/IM correspondence for the Fateev model
• On the Harish-Chandra homomorphism for infinite-dimensional Lie algebras
• Higher-spin conserved currents in supersymmetric sigma models on symmetric spaces
• The argument shift method and the Gaudin model
• Lie algebras and equations of Korteweg-de Vries type
• Unitary representations of the Virasoro and super-Virasoro algebras
• Unitary reflection groups and cohomology
• Arrangements of hyperplanes and Lie algebra homology
• Gaudin model, Bethe ansatz and critical level
• Spectra of quantum KdV Hamiltonians, Langlands duality, and affine opers
• Local charges in involution and hierarchies in integrable sigma-models
• Spectral curves, opers and integrable systems.
• Higher-level eigenvalues of \(Q\)-operators and Schrödinger equation
• Quantum sine(h)-Gordon model and classical integrable equations
• Cubic hypergeometric integrals of motion in affine Gaudin models
• Cyclotomic Gaudin models with irregular singularities
• Critical points of master functions and integrable hierarchies
• Bethe ansatz and the spectral theory of affine Lie algebra-valued connections. I: The simply-laced case
• Gaudin models with irregular singularities
• Vertex Lie algebras and cyclotomic coinvariants
• Schubert calculus and representations of the general linear group
• Quantization of soliton systems and Langlands duality
• Critical Points of Master Functions and the mKdV Hierarchy of Type A 2 (2)
• Integrals of motion from quantum toroidal algebras
• Anharmonic oscillators, the thermodynamic Bethe ansatz and nonlinear integral equations
• The ODE/IM correspondence
• Commuting charges and symmetric spaces
• Conserved charges and supersymmetry in principal chiral and WZW models
• Integrable sigma-models and Drinfeld-Sokolov hierarchies
• Spectral determinants for Schrödinger equation and \({\mathbb{Q}}\)-operators of conformal field theory
• Local conserved charges in principal chiral models

This page was built for publication: Affine Gaudin models and hypergeometric functions on affine opers